Although I am a numbers guy, the casual way in which politicians and reporters are throwing the word “trillion” around has attracted my attention. Big numbers are hot news these days, so I thought it would be useful to my readers to examine some of the numbers we are currently seeing and hearing about.
How much is a billion? Most people know that a billion is the number 1,000,000,000. Mathematicians would say it is 10 to the 9th power (or 10 multiplied 9 times). You can think of it as a thousand millions – or a million thousands. But that’s different from understanding the number quantitatively. We know what a hundred yards is, or even what a mile is (5280 feet). These are graspable quantities in the everyday world. Think of it this way: if you could spend $1000 a day, how long would it take to spend $1 billion?
Answer: Just over 2700 years – i.e., a million days. Think you could do it, should you live so long? Well, maybe. A thousand bucks a day is $365,000 a year. Some people have incomes like that – not tons of people, and maybe none in your acquaintance, but there some besides athletes or film stars.
The example breaks down, though, because it ignores the small detail of “interest.” If you actually had a billion dollars, you would surely invest it in some kind of interest-paying financial instrument. A modest rate of return might be 3%. That would produce interest of $30 million a year. Whoa! That’s way over the measly $365,000 a year you’re trying to spend. A bundle like that would fund handsome incomes of $300,000 a year for 100 families, leaving the principal intact. When we start talking billions, we’re really talking about BIG money – way beyond the comprehension of most of us.
What about a trillion? It was not until the Obama administration burst on the scene that we started talking about trillions of dollars with any regularity. Politicians and the media now toss the number around nonchalantly, but can anybody really understand how much money that is? A trillion is 10 to the 12th power. That would be enough to give a share of $10,000 to each of 100,000,000 people – or a share of $3,333 to each of 300,000,000 people. (The latter is the approximate population of the USA.)
A trillion bucks invested at interest of 3% would earn $30 billion a year interest – a pretty nice income of $100,000 a year for 300,000 families. No matter how you slice it (to paraphrase the late Senator Evertt Dirksen): “…a trillion here and a trillion there – before you know it you’re talking about real money.”
Gazillions. Here are the names of some gazillions in the base-10 system we use:
- 1 Billion = 109 = 1,000,000,000
- 1 Trillion = 1012 = 1,000,000,000,000
- 1 Quadrillion = 1015 = 1,000,000,000,000,000
- 1 Quintillion = 1018 = 1,000,000,000,000,000,000
- 1 Sextillion = 1021 = 1,000,000,000,000,000,000,000
How big is the ocean? During Obama’s terms, the ocean got a lot of media attention because a ruptured oil well in the Gulf of Mexico had spilled an awful lot of oil. There was much hand-wringing about the “destruction” of the Gulf’s ecosystem. Some alarmists said it might take decades – even centuries – for the Gulf to recover from the leaked oil. Some wild-eyed prophets said the Gulf would become a “dead sea” that would never recover.
There’s no doubt that a lot of oil spilled out before the leak was capped. Figures vary on the quantity, but 4.9 million barrels seems to be a consensus number. That’s 205 million gallons. It’s staggering, and I wouldn’t try to argue otherwise. We can write the number, but the amount of oil it represents boggles the mind.
Was it enough oil to “destroy” the Gulf of Mexico? Probably not. Part of the problem reporters, pols, and the general public have is a lack of understanding of how big the Gulf of Mexico – or, indeed, the ocean – really is. The Gulf of Mexico contains 597,834 cubic miles. So how much water is that? We know that –
- A cubic foot = 7.5 gallons (yes, it’s true);
- A mile = 5,280 feet; and
- A cubic mile = 5,280 ft. x 5,280 ft. x 5,280 ft. = 147.2 billion cubic feet;
- So a cubic mile contains 1.104 trillion gallons;
- Thus, the Gulf of Mexico’s 597,834 cubic miles contain 660 quadrillion (660,000,000,000,000,000) gallons of water.
This puts the Gulf’s Deepwater Horizon spill in perspective. 205 million gallons was a lot of oil, but compared to 660 quadrillion gallons of water in the Gulf, it’s relatively little.
Beyond the hugeness of the Gulf, the ocean’s primary defense against pollution is its ceaseless churning – a kind of “grinding” action which “emulsifies” oil into microscopic particles that become lost in the sea’s vastness. This explains why those catastrophic predictions about the Gulf oil spill didn’t happen. Except for small amounts of oil that reached land, the oil spilled from Deepwater Horizon has disappeared.
Of course, the entire ocean is much bigger than the Gulf of Mexico. The ocean’s volume is difficult to measure, so estimates vary, but 1.347 billion cubic kilometers – give or take a few million km3 – is probably a good estimate. For readers who don’t think well in metric units, that’s roughly 323,000,000 cubic miles – or 356.6 quintillion (i.e., 356,600,000,000,000,000,000) gallons of water
This is where most readers’ eyes glaze over. (In fact, mine are a little glazed, too.) What I want to convey is that the ocean is unimaginably vast. Understanding that – even if the numbers are beyond our grasp – will help us to avoid being deceived by bogus claims of terminal catastrophe.
How big is the atmosphere? The preceding data on the size of the ocean is useful in the context of today’s discussions about the climate. Experientially, we know that the ocean is vast because many of us have waded in it, swum in it or sailed in it. If you’ve flown high above it – with no land visible in any direction – you get some idea of how big it is.
But failure to grasp the size of the atmosphere is more common among politicians, reporters and the general public. Part of our difficulty is that we “see” only a small dome of atmosphere from wherever we stand on the earth. If a person’s eyes are about six feet above the surface of the earth, then his horizon of visibility is typically about 3 miles away. This atmospheric “window” for the ordinary person is quite small, compared with the size of the atmosphere. Our misperception lets us be deceived about effects of emissions like CO2 which are relatively small.
The ocean covers about 75% of the globe’s surface. It’s no more than 7 miles deep anywhere, and much less in most places. But the atmosphere covers the entire globe and is a radial layer (like an orange peel) above the earth. Estimates of the atmosphere’s size vary, depending upon how high you think it goes, but 60 miles high seems to be a mutually agreeable number. Using 4,000 miles as the earth’s radius, a 60 miles high atmosphere has volume of 12.246 billion cubic miles.2 That’s 13,600,000,000,000,000,000,000 (i.e., 13.60 sextillion) gallons, or 38 times the ocean’s size.
These volumes can’t be comprehended by most of us. But the knowledge that the atmosphere is far larger than the ocean – which we know is immense – should help us understand that our “emissions” are relatively puny, in comparison. And like the ocean’s protective “grinding” motion, the atmosphere’s constant storms and weather-movement grind up and distribute emissions from the earth.
Scientists have noted that if all human-produced carbon dioxide emissions stopped, the reduction would constitute only 3% of all CO2 being released into the atmosphere. All the rest comes from natural sources. In other words, elimination of all human life would produce only a trivial reduction in emissions and no measurable change in temperature. Also, the claim that CO2 emissions are causing storms of increasing strength is a politically useful tale which scientists have repeatedly debunked via historical data.
All this is not to say that it’s OK to pollute and despoil the earth, the oceans or the atmosphere. We know better than that. A great deal of good work has been done since the 1960s to reclaim places like Lake Erie, which had been polluted almost to death before new environmental programs enabled its recovery. The catalytic converter for automobiles also stopped emission of nitrous oxide pollutants which caused those terrible smog-alert days of the 1970s.
But environmental activists’ pot-dream that we can “stop climate change” or “save the oceans” by paying crushing taxes and destroying our economy is another matter entirely. As citizens, we need to understand that the awesome size of oceans and atmosphere place them beyond our puny reach, and that both realms have their own natural cleansing mechanisms. Most politicians don’t know those gigantic sizes of oceans and atmosphere, but we’d better. We need to consider these matters with as much factual knowledge as possible before we let lawmakers pursue a fiscal course that will accomplish nothing but ruin.
- If your eyes are h feet above the earth’s surface (see diagram), then
(r+h)2 = d2 + r2 ,
where r is the earth’s radius, and d is the distance to the visible horizon.
So d2 = h(2r + h), and d = [h(2r + h)]1/2
Solved in units of feet, where
h = any height in feet
r = 4000 × 5280 = 21,120,000 feet
e. g., if h = 1,000 feet (like the Empire state building)
Then d = 205,526 feet = 38.9 miles
2. Size of the atmosphere:
If earth’s radius is 4000 miles and the atmosphere is 60 miles thick,
Then earth’s volume = (4pi /3)× (4,000)3 = 268.082 billion cubic miles
And volume of earth + atmosphere = (4 pi/3) × (4,060)3 = 280.318 billion cubic miles.
So volume of the atmosphere = (280.33 – 268.08) billion = 12.25 billion cubic miles
= 13.60 × 1021 gallons